Anomaly detection using dependence trees and copulas

Details

Supervisors

Segers, Johan

Faculty

Faculté des sciences

Degree label

Master [120] en science des données, orientation statistique, à finalité spécialisée

Abstract

In this master's thesis, the use of dependency trees with copulas for anomaly detection is studied. In particular, two algorithms are detailed: the HKMN by Horváth et al. (2020) and the VCAD introduced in this thesis. The VCAD combined the work of Horváth et al. (2020) that introduced copula-trees in anomaly detection with the pair copula constructions (Joe 1996; Bedford and Cooke 2001; Bedford and Cooke 2002). The aim of the thesis is to verify the efficiency of copula-trees in the field of anomaly detection and to investigate the impact of building vines rather than standalone copula-trees for this task. In the first part, we recall the theoretical concepts associated with these dependence trees and copulas. Previous works on dependence trees are presented, such as the Chow-Liu trees or the pair copula constructions. Then, the two studied algorithms are explained and implemented. In Part II, an evaluation of the algorithms is performed on seven datasets. The results produced in this phase are encouraging as our implementations of HKMN and VCAD match and sometimes even outperform the competing anomaly detection methods. One of the striking features of these implementations is the consistency of their performance. Where some competing algorithms might shine in one context and then fail in another, the HKMN and VCAD maintain a consistent performance that appears to be independent of the specific characteristics of the dataset under study. Afterwards, we present the limitations of HKMN and VCAD but also their advantages.